Let's start by understanding the problem:
1. We're given that point [tex]\( E \)[/tex] has a coordinate of 2.
2. The length [tex]\( EG \)[/tex] is 10.
To find the possible coordinates of point [tex]\( G \)[/tex], we need to consider both directions along the number line from point [tex]\( E \)[/tex]. Point [tex]\( G \)[/tex] could be either to the right or to the left of point [tex]\( E \)[/tex].
### Step-by-Step Solution
1. Right Direction:
- If point [tex]\( G \)[/tex] is to the right of point [tex]\( E \)[/tex]:
[tex]\[
\text{Coordinate of } G = \text{Coordinate of } E + EG
\][/tex]
[tex]\[
G = 2 + 10
\][/tex]
[tex]\[
G = 12
\][/tex]
2. Left Direction:
- If point [tex]\( G \)[/tex] is to the left of point [tex]\( E \)[/tex]:
[tex]\[
\text{Coordinate of } G = \text{Coordinate of } E - EG
\][/tex]
[tex]\[
G = 2 - 10
\][/tex]
[tex]\[
G = -8
\][/tex]
By considering both the right and left possible locations for point [tex]\( G \)[/tex], we find that the coordinates for [tex]\( G \)[/tex] could be:
[tex]\[
12 \text{ or } -8
\][/tex]
### Final Answer
The possible coordinates for [tex]\( G \)[/tex] are [tex]\( \boxed{12, -8} \)[/tex].
